Radical Radicals

I finished up my unit on Systems of Equations before the Thanksgiving break and was left with a two-week window before the district said I had to give a Mid-Year Exam. The pacing guide had us starting polynomials and quadratics, but that was not a unit I wanted to break up over the Christmas break, so I decided to spend these two weeks on Radicals. In the past two years, I have crammed in Radicals right before we start reviewing for the EOC, so I liked having the unit at this time instead because I didn't feel so rushed. Coming off Systems of Equations, this was also a chance for students to catch their breath with an easier concept -- before we head into quadratics and really blow their minds ;)

We started with a quick review of the Laws of Exponents and this free foldable. I added some notes for students to fill in summarizing the rule for each step before I sent it to the copier.  
I showed them how to expand each problem and then asked them to come up with the rule, which helps them to visualize what's going on, and gives them a strategy to go back to when they forget the rule.

Negative and Zero exponents always throw students for a loop, so they needed their own sheet of notes. I loved this post from Scaffolded Math and Science about Negative Exponents. We did these three problems and then I asked students to find the rule. We continued the pattern to see that what happens when you have negative exponents. 

Again, the students summarized the rule and had a pretty good understanding. So I put them to the test with this puzzle
I love listening to students talk about these problems and watching their understanding grow. 

We finished up with a word problem about exponential growth. I love how this problem has students interpret what the negative exponents mean in the context of this word problem - I was proud that students in each class came to the conclusion that negative exponents would indicate time before the experiment started. It also helps them solidify the idea that a zero exponent doesn't equal zero, because it represents the starting point.

Day 2, it was time for radicals! Like last year, I was determined not to teach a trick. I showed them both how to simplify with prime numbers and perfect squares. I write out a lot of steps, and often students find ways to simplify and shorten once they understand what they are doing. I also made a point of explaining every step. "The square root of 2 squared is 2, so I can simplify it as a whole number outside the radical. But the square root of 5 is an irrational number, so I leave that inside the radical." By repeating this step (what seemed like a million times), I didn't have students trying to bring the number with its exponent outside the radical. I did, however, still have some students tricked by this check all that apply.
That last problem always leads to a debate, but I had far less students thinking it was correct that in years past. We practiced simplifying radicals with this coloring activity. I love that the answer bank allows students to self-check as they go. There is nothing worse than practicing a skill incorrectly, so I like when they have to stop and find their mistake when their answer doesn't match one of the choices. Plus the coloring provides a nice brain break!

For Day 3, I put a problem up on the board with variables inside the radical and asked students to decide what to do. I've been focusing a lot on hooking everything to their prior knowledge. Someone suggested expanding x^3, and then students could see variables were really no different than dealing with factors. I love these Check All That Apply question types for this topic.

After a few examples, they practiced with a puzzleStudents had to be careful to "attend to precision" because several of the problems and answer choices were similar. This forced students to really focus on their exponents and see the difference between having x^3 inside a radical and x^4. It also meant that students didn't have to keep re-creating a factor tree for each problem. I heard great discussions about what happens when the radical has a coefficient in front of it too.

Next we moved on to Operations on Radicals - adding, subtracting and multiplying them, which I introduced with these fun {FREE} Interactive Notes. Students practice applying the operations on radicals to find the area and perimeter of shapes - and the shapes are super fun to color! 
We also did some regular practice problems on the neighboring page. 

Students practiced with a Versatiles activity and then completed an exit ticket/ mini quiz. Here is a link to the exit tickets if you want to use them.

That left us with one day left for review/wrap up. I love having an extra catch-up day like this at the end of the unit. The exit ticket provided me with some great data for who needed remediation (students who had been absent for a few days were super confused) and who was ready for some enrichment. I reminded students that so far we had been dealing with square roots, which have an index of 2, and then I presented a problem with an index of 3 and asked students how they thought it would be different. Then I did one with an index of 4 - they knew right away what to do. 

Next students completed a variety of assignments -  those who needed help completed this maze. I love how they receive instant feedback by finding their answer in one of the arrows. This maze was perfect for those students still struggling with the overall concept or students who had missed a couple classes over the two -week period. 

Some students wrapped up the Simplify Radicals Coloring Activity from earlier in the week. Those who were up for a challenge took on the Operations on Radicals Coloring Activity. Again with the answer bank, this time in the flower petals. 

Students with extra time answered some pennant problems - these are my go-to when I have a few minutes left at the end of class that needs to be filled. Plus students love decorating them and seeing their work on display on the walls and halls.

I also gave students the option to retake the Exit Ticket/ Mini Assessment if they were unhappy with their grade or thought they could do better. I love giving students the opportunity to challenge themselves to get a better score, and to see improvement. Sometimes just one class period makes all the difference in their understanding - like this student who went from a 50% to a 100% :) Totally RADICAL!

When old toys get new life in the classroom

A few weekends ago was our neighborhood garage sale. I am always on the lookout for fun stuff for my classroom, and I picked up this fun thing called a Perplexus for 50 cents. I wasn't exactly sure how it worked but it looked intriguing and like it involved some problem solving skills, and for 50 cents, I couldn't pass it up.

I wasn't exactly sure what to do with it, so I just set it out in my student supply area the pencil sharpener and cup of pencils and didn't think anything of it. A student in my 1st period who sits up front immediately noticed and asked, "Can I try that if I finish my work early?" I told him, "Of course," and as soon as he finished he grabbed the Perplexus. A few students saw him doing it and leaned over to watch. Now students will come in during passing period instead of roaming the halls to play with it. It's a 3-D maze that you have to guide the ball through and definitely requires thinking ahead and problem solving because the track flips and turns and there are lots of obstacles on the way to the bucket in the center.

This thing has become such a hit with my students, and to think just a few weeks it was collecting dust in someone's closet. I started to look around my own house at some toys that have fallen out of favor to see if they could be given new life in a different setting. I asked my son's preschool teacher if she wanted this puzzle and lacing beads for her classroom and she was very excited to have them. My son isn't interested in them at home, but he might be at school, and, like me, his teacher will enjoy having something new and fun to entertain her kiddos.

Reflection: How do you think you did on this test? Why?

I hate grading tests! I've tried to trick myself into having fun doing it by buying cool pens to grade with, sitting in a comfy chair, eating a snack. I even tell myself the lie that, "I could go home and grade them on my couch," and then the tests make a round-trip from home to school without ever leaving my school bag. There is ONE thing I do love about grading tests though, and it's the last question I put on every test and quiz.

"Reflection: How do you think you did on this assessment? Why?"

Here are some reasons why I love this question:
1. Metacognition - thinking about thinking. Students have to reflect on what they learned and how the learned it and decide how that translated to the assessment. This student knew which questions she struggled with (both content and question type)

2. Ownership in student learning - I'm a firm believer that students should be the one driving most of the work in my classroom. If they didn't learn what they needed to in order to be successful, I want to know why they think that happened. 
Also if they feel they successfully mastered a skill, I want to know why they think that happened as well.

3. Accountability - I love when students tell me what they could do differently to improve the outcome. This student says, "I should have spent more time studying the study guide. No doubt this is the grade I deserve."

4. Insight - Sometimes students are willing to write things that they wouldn't say out loud. Language arts teachers already know this, but math teachers don't have as many opportunities for them to open up with writing. This open-ended question lets them express anything, like this student who was just having a bad day.

5. Easy points -  As long as they answer it, they will get it right. No hunting for errors or partial credit, this is a point everyone can get. I always remind them that they do get credit as long as they answer the question and tell them, "Don't miss that one, it's the easiest question on the test." 
 6. Teenagers are funny - I already know this by spending all day with them, but sometimes they will write some hilarious things.
I hope you will give a question like this a try sometime on a test or quiz, you may just be surprised at what your students have to say.

Old Math Guy

Last week we gave the PSAT to all the 10th and 11th graders at our school. The seniors had a special assembly and freshmen reported to their homeroom class. The homerooms are assigned by building alphabetically, so the students in our homeroom are usually not in any of our classes. I happened to have a sophomore homeroom this year, so I spent the morning proctoring the PSAT. [I swear three minutes sometimes seems like an eternity when you waiting for the session to end.] Needless to say, it was a long day. So testing ate up the first four hours of the day, then I saw my Geometry class and then one of my five algebra classes for only an hour (classes are usually 90 minutes). By the end of that day, everyone was fried - my students had either spent the morning testing or sitting in their homeroom bored.  But I do not ever give free days, so I knew I wanted to do something that will help them with the linear functions unit we were working on, but a standard lesson was not going to hold their attention today.

My friend, Amanda, at Free to Discover, has an awesome set of products called, "Old Math Guy," that I have been wanting to try out, and this was the perfect opportunity. I decided on Matching Linear Graphs to Equations in Slope Intercept Form.  I asked the kids if anyone knew how to play "Old Maid," and a few said they did. I had a few kids tag-team explaining the rules of "Old Maid." Then one of my students said, "Did you bring in cards for us to play Old Maid?" I nodded. Then he said, "Wait, these are going to have math problems on them, aren't they?" I said, "Of course they are!" The rules are the same as Old Maid - they look for matches and lay them down and they draw from their neighbors hand until all the cards are out and someone ends up with the Old Math Guy.

My students had a lot of fun with this activity, and I overheard some great conversations about what made a "match." The students would watch each other like hawks to make sure their equations really matched their graphs (attend to precision!). Some students had good poker faces with Old Math Guy and some didn't. They all had fun, and it was a great brain break for the end of a long, off-schedule day.

I think this is a great engaging activity that I cannot wait to use again! With the holidays coming up, we need a lot of tricks up our sleeve, and this one kept their attention and allowed for great practice in a unique way.

Amanda even has a freebie in her store to try out with your kiddos: Old Math Guy Translating Algebraic Expressions 

Math-y Door Decor

Last week is annual "Jacksonville Goes to College Week," so our guidance counselors challenged us to a door decorating contest. I typically write those off as, "Ain't nobody got time for that," but I had such luck with my Christmas Door Decorations that I wanted to give it a try. Just like when I did my Christmas door, I also did not want to lose any instruction time. Scaffolded Math and Science had the perfect solution for me - a Slope Tree, which fit right into our Linear Functions unit.

I gave each student a leaf and they found the slope between two points and then decorated it. It was a nice exit ticket for our class on slope. We put them all together to make a tree.

The idea for my "pun-ny" sign actually came a student who said, "If this is an exit ticket, can we 'leaf' when we finish it." I took that and said, "We are ready for college when we 'leaf' ACHS." Then one of my students added some color to it when she finished a test early.

I think it turned out great - a perfect fall decoration! And best of all - no instructional time was lost in the making of this awesome math-y door decor!
P.S. If you are looking for those awesome Welcome sign letters, they are from Math=Love here 

Hurricane Matthew: From Inside the Cone of Uncertainty

I grew up in the Midwest and left 10 years ago, trading the brutal winters for year-round sunshine. Although we have had a few near-hurricanes and tropical storms in my time as a Floridian, nothing has hit close to home like Hurricane Matthew. I live in Jacksonville, Florida about five miles from the coast, where we can afford a house but can also have our toes in the sand in 10 minutes flat, with my husband (also a teacher and a native Floridian) and our two children, 4 and 1.

On Monday, my husband texted me this picture and we talked vaguely about what would happen if the hurricane actually came near us in Jacksonville, but we didn't make any real plans.

On Tuesday, the clouds over my school looked a little ominous in the morning. The storm path hadn't changed much, so I stopped at the grocery store after school to stock up on water, snacks, and batteries and I filled my gas tank with a short wait.

By Wednesday, the mood around campus was that of uncertainly - Matthew had already torn through Haiti and Cuba and its strength was undeniable. The forecast path brought it closer to home. The students minds were filled with "What ifs" and I must have been asked if school would be canceled at least 50 times. Imagine teaching the day before a holiday break and multiply it by 10, that's how distracted these students' minds were, and mine was too. I was filled with uncertainty of what the weather would bring for me and my family and what decisions I should be making. I had a quiz scheduled (the end of the 1st quarter is nearing next week), but everyone was so preoccupied that I decided to make it open notes. I tried to make my lesson on slope as low-key as possible, we watched the Adventures of Slope Dude, took some notes and practiced with a Versatiles activity. I found that the kids needed the distraction as much as I did as the rain outside beat against the windows.
By the end of the last period of the day, the principal announced that school was canceled for Thursday and Friday and everyone, teachers included, needed to be off campus by 2:30. Leaving was so nerve-racking, not knowing what I would come back to. I unplugged everything, took a few pictures of my possessions, and headed out.
The few times I get to leave school at 2:30, I usually zip home and have free reign over all the stores. Today traffic was already building on the highways, and the line at the gas station stretched out onto the road with at least 10 cars waiting in each direction. I was happy to have already taken care of these stops earlier. When I got home, the news now projected this path:
Being a math teacher, I like making decisions based on odds and probability of events occurring, but it seemed like every time I looked at the news, the odds were changing. The meteorologists were giving the hurricane a 15 percent chance of making landfall in Jacksonville as a Category 4 storm. As I tried to go to bed that night - I began to truly understand the term "Cone of Uncertainty." Did it make sense for our family to leave town? Where would we go - we have family near Orlando and Tampa, but would the weather be just as bad there? And what would traffic be like as we went there and returned home after the storm? What if the storm did significant damage to our house and no one was there to protect it because we had left? What is the storm did significant damage to our house and we were there with our two babies? What would it be like to have two small children without power in our house? Would I be able to remain calm if a true category 4 hurricane came through? 

I decided to pack a bag with clothes for everyone for five days, snacks and water, and all my hard drives of family photos, and sleep on the decision. I woke to find this on my phone: 
The uncertainty was too much, and I knew staying and waiting would make me a nervous wreck for the next few days, which I knew would have a 100% chance of negatively impacting my parenting skills. My husband decided to stay back and board up the house and deal with any damages or issues, and I buckled the kids in their car seats and hit the road for Grandma's house. My mother-in-law lives just south of Orlando and their weather forecast called for 35 mph winds and rain, which sounded much better than the 100 mph winds that could be possible in Jacksonville. I decided that the worst-case scenario of evacuating would be a traffic jam, and the worse-case scenario of staying was being huddled into the bathroom with my two little ones as a tree crashed through our roof. 

My husband weathered the storm at home without ever losing power. The wind was fierce and the rain was relentless, but our house escaped unscathed, except for some downed tree branches and mud puddles in our backyard. Many of my friends and neighbors were not so lucky.

Today my husband asked me, "If you had this to do over again, would you do it the same?" Again comes that "Cone of Uncertainty," did I make the right decision? Did I over-react by leaving? Was it overkill to board up our windows?  As a math teacher, my brain is trained to be analytical, but Mother Nature cannot be tied down with logic and reason. I do know that as this storm shifted countless times with different trajectories, I was happy to be watching from a safe distance away. 

How a hole puncher saved the day: Proving Lines Parallel Proof Activity

Even in the 7th week of school, Geometry proofs still strike fear into my little freshmen. For today's lesson on proving lines parallel, I knew I wanted them to do proofs. I found this great cut and paste activity from Amazing Mathematics. I chose to print the version that has the statements filled in and students only have to come up with the reasons for each step. By the time we get to triangle congruence, they will be writing both sides, but I was OK with giving them the outline today.

We reviewed all the theorems and converses and theorems and did a few examples together in their interactive notebooks, and then I set them lose on the proofs. I have my students grouped in threes, which is plenty of brain power to figure out these proofs. I gave each group a strip of paper and had them write the numbers 1-6 on it. Each group started with a proof (I only used 1-4 in the first round because they get increasingly more difficult). They worked together to correctly place the reasons in the proof. When the group agreed, they called me over for a check.

If it was right, I took my blue marker and scribbled off the number of the proof they finished. Then I saw a student look the other blue markers in my supply box with a gleam in his eye. And I realized with this system, there is no way I would be able to keep them from cheating. I changed the scribble to my initials, and then I had a better idea... I dug into the depths of my desk drawer and I got out my single hole puncher and punched a hole over the number when they completed it. The students LOVED it! It's amazing how something so simple totally changes the game. Then they wanted to use the hole puncher - and they would fight over whose turn it was to make the punch. The click of the puncher and the creation of the hole was as satisfying as correctly completing the proof. After I (or they) punched the number, they scrambled up the pieces and took it to the middle table and exchanged it for another proof. They kept doing this until they finished all six proofs.

Typically telling students they would be completing six Geometry proofs to prove lines parallel would be met with moans and groans, but my students were very engaged and motivated to finish the problems. I definitely see my hole puncher making future appearances in class!

Next they are going to try out this Proving Lines Parallel Crossword Puzzle. The outline of the proof is still there, but they have to come up with some missing statements and reasons. They still get the self-checking benefit of the crossword puzzle though.

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